Problem: If $x \odot y = 4x-8$ and $x \barwedge y = 2x-3y$, find $(-2 \odot -4) \barwedge 2$.
Explanation: First, find $-2 \odot -4$ $ -2 \odot -4 = (4)(-2)-8$ $ \hphantom{-2 \odot -4} = -16$ Now, find $-16 \barwedge 2$ $ -16 \barwedge 2 = (2)(-16)-(3)(2)$ $ \hphantom{-16 \barwedge 2} = -38$.